Finite Group DatabasebetaFinite Group Databasebeta| order | 18774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C149 · Schur multiplier (H2) = C1 |
| direct product | C7×D9×C149 |
| unambiguous semidirect product | C9⋊(C2×C7×C149) |
| Fitting, Hall | C7×C9×C149 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C7×C149 |
| Hall | C9×C149 ⋊ C2×C7 |
| Hall | C7×C9 ⋊ C2×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C149 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C7×C149 |
| Frattini | C3 | D3×C7×C149 |
| Fitting | C7×C9×C149 | C2 |
| socle | C3×C7×C149 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C7×C149 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9387 |
6258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D149, D7×D9×C149, D9×D1043, … |
| maximal normal subgroup of | C7×D9×D149, D7×D9×C149, D9×D1043, … |
| maximal quotient of | C7×Dic9×C149, C2×C7×D9×C149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18774, 6);